Answer:
<em>Exact Form:
</em>
![\frac{8}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B8%7D%7B3%7D)
<em>Decimal Form:
</em>
![2.6](https://tex.z-dn.net/?f=2.6)
<em>Mixed Number Form:
</em>
Hope this helps :)
<em>-ilovejiminssi♡</em>
Create a system of equations
x + y = 123
5x + y = 343
I use substitution
y = 123 - x
5x + 123 - x = 343
4x + 123 = 343
4x = 220
x = 55
Plug in
x + y = 123
55 + y = 123
y = 68
Check
5x + y = 343
5(55) + 68 = 343
275 + 68 = 343
343 = 343
Answer:
![\text{Length of median AD}=\sqrt{37}](https://tex.z-dn.net/?f=%5Ctext%7BLength%20of%20median%20AD%7D%3D%5Csqrt%7B37%7D)
Step-by-step explanation:
We are given the vertices of triangle ABC. We need to find the length of median AD.
Please see the attachment for figure.
D is mid point of BC because median bisect the opposite side of triangle.
Using the formula of mid point. we get coodrinate of D
![\text{Mid Point :}\left ( \frac{x_1+x_2}{2},\frac{y_1+y_2}{2} \right )](https://tex.z-dn.net/?f=%5Ctext%7BMid%20Point%20%3A%7D%5Cleft%20%28%20%5Cfrac%7Bx_1%2Bx_2%7D%7B2%7D%2C%5Cfrac%7By_1%2By_2%7D%7B2%7D%20%5Cright%20%29)
D is mid point of B(1,5) and C(-3,-1)
![\therefore D \left ( \frac{1-3}{2},\frac{5-1}{2} \right )\Rightarrow (-1,2)](https://tex.z-dn.net/?f=%5Ctherefore%20D%20%5Cleft%20%28%20%5Cfrac%7B1-3%7D%7B2%7D%2C%5Cfrac%7B5-1%7D%7B2%7D%20%5Cright%20%29%5CRightarrow%20%28-1%2C2%29)
AD is median of triangle ABC. Now we find length of median AD using distance formula of two coordinate.
![\text{Distance }=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=%5Ctext%7BDistance%20%7D%3D%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
A(5,1) and D(-1,2)
![AD=\sqrt{(5+1)^2+(1-2)^2}\Rightarrow \sqrt{36+1}](https://tex.z-dn.net/?f=AD%3D%5Csqrt%7B%285%2B1%29%5E2%2B%281-2%29%5E2%7D%5CRightarrow%20%5Csqrt%7B36%2B1%7D)
![\text{Length of median AD}=\sqrt{37}](https://tex.z-dn.net/?f=%5Ctext%7BLength%20of%20median%20AD%7D%3D%5Csqrt%7B37%7D)
Thus, ![\text{Length of median AD}=\sqrt{37}](https://tex.z-dn.net/?f=%5Ctext%7BLength%20of%20median%20AD%7D%3D%5Csqrt%7B37%7D)
-4 is the negative and 3 is the positive if I see correctly.